Notice that compared to the deep BSDE approach in [1]}, which considers a loss function from the misfit between the l.h.s (the target) and r.h.s. of (REF ) at time 0, namely
\( \begin{split} \tilde{L}^*_{DBSDE}(y_0,\delta ) & := \; {\mathbb {E}}\Big [ \big | Y_T^{*,0} - y_0 - \int _0^T {\mathcal {Z}}^\delta (s,X_s^*)^\top \sigma ^{\mathrm {a}^*}(s,X_s^*) {\rm d}W_s \big |^2 \Big ],\end{split} \) 
